Find all roots of the polynomial $2x^3-3x^2-5x+6$

Step 1 ：Step 1: Identify the coefficients of the polynomial and list them. The coefficients are 2, -3, -5, and 6.

Step 2 ：Step 2: List the factors of the constant term (6) and the leading coefficient (2). The factors of 6 are $\pm 1,\pm 2,\pm 3,\pm 6$ and the factors of 2 are $\pm 1,\pm 2$.

Step 3 ：Step 3: Form the ratio of each factor of the constant term to each factor of the leading coefficient. The potential rational roots are $\pm 1,\pm 2,\pm 3,\pm 6,\pm \frac{1}{2},\pm \frac{3}{2}$.

Step 4 ：Step 4: Substitute each potential root into the polynomial until you find one that makes the polynomial equal to zero. After testing, we find that 1, -2 and 3 are roots of the polynomial.

Step 5 ：Step 5: Therefore, the roots of the polynomial $2x^3-3x^2-5x+6$ are 1, -2, and 3.